In order to study the deformation displacement and the stress field of brittle rocks under harmonic dynamic loading, a series of systematic numerical simulations are conducted in this paper. A 3D uniaxial compression simulation is carried out to calibrate and determine the property parameters of sandstone and a model of the cylindrical indenter intruding the rock is proposed to analyze the process of elastic deformation. Four main parameters are taken into account, namely the position on the rock, the frequency and the amplitude of dynamic load, the type of indenter and the loading conditions (static and static-dynamic). Based on the analysis undertaken, it can be concluded that both of the deformation displacement and stress field of the rock change in a harmonic manner under the static-dynamic loads. The frequency and the amplitude of harmonic dynamic load determine the period and the magnitude of the rock response, respectively. In addition, the existence of harmonic dynamic load can aggravate the fatigue damage of the rock and allow a reduction in static load. Our investigations confirm that the static-dynamic loads are more conducive to rock fracture than static load.